The Sensitivity of Bank Net Interest Margins and Profitability to Credit, Interest-Rate, and Term-Structure Shocks

Across Bank Product Specializations

Gerald Hanweck Professor of Finance

School of Management George Mason University

Fairfax, VA 22030 ghanweck@gmu.edu

and Visiting Scholar

Division of Insurance and Research FDIC

Lisa Ryu Senior Financial Economist

Division of Insurance and Research FDIC

lryu@fdic.gov

January 2005

Working Paper 2005-02

The authors wish to thank participants at the FDIC’s Analyst/Economists Conference, October 7–9, 2003, and at the Research Seminar at the School of Management, George Mason University, for helpful comments and suggestions. The authors would also like to thank Richard Austin, Mark Flannery, and FDIC Working Paper Series reviewers for their comments and suggestions. All errors and omissions remain the responsibility of the authors. The opinions expressed in this paper are those of the authors and do not necessarily reflect those of the FDIC or its staff.

mailto:ghanweck@gmu.edumailto:lryu@fdic.gov

The Sensitivity of Bank Net Interest Margins and Profitability to Credit, Interest-Rate, and Term-Structure Shocks Across Bank Product Specializations

Abstract

This paper presents a dynamic model of bank behavior that explains net interest margin

changes for different groups of banks in response to credit, interest-rate, and term-structure

shocks. Using quarterly data from 1986 to 2003, we find that banks with different product-line

specializations and asset sizes respond in predictable yet fundamentally dissimilar ways to these

shocks. Banks in most bank groups are sensitive in varying degrees to credit, interest-rate, and

term-structure shocks. Large and more diversified banks seem to be less sensitive to interest-rate

and term-structure shocks, but more sensitive to credit shocks. We also find that the composition

of assets and liabilities, in terms of their repricing frequencies, helps amplify or moderate the

effects of changes and volatility in short-term interest rates on bank net interest margins,

depending on the direction of the repricing mismatch. We also analyze subsample periods that

represent different legislative, regulatory, and economic environments and find that most banks

continue to be sensitive to credit, interest-rate, and term-structure shocks. However, the

sensitivity to term-structure shocks seems to have lessened over time for certain groups of banks,

although the results are not universal. In addition, our results show that banks in general are not

able to hedge fully against interest-rate volatility. The sensitivity of net interest margins to

interest-rate volatility for different groups of banks varies across subsample periods; this varying

sensitivity could reflect interest-rate regime shifts as well as the degree of hedging activities and

market competition. Finally, by investigating the sensitivity of ROA to interest-rate and credit

shocks, we have some evidence that banks of different specializations were able to price actual

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and expected changes in credit risk more efficiently in the recent period than in previous periods.

These results also demonstrate that banks of all specializations try to offset adverse changes in

net interest margins so as to mute their effect on reported after-tax earnings.

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1. Introduction

The banking industry has undergone considerable structural change since the early 1980s

as the legislative and regulatory landscape governing the industry has evolved. The structural

changes, in turn, have had significant effects on the degree of market competition and the scope

of products and services provided by banks as well as significant effects on the sources of bank

earnings. Despite these developments, credit and interest-rate risks still largely account for the

fundamental risks to bank earnings and equity valuation as well as to the contingent liability

borne by the FDIC insurance funds. The relative importance of credit and interest-rate risks for

bank earnings and the FDIC’s contingent liability has varied over time in response to changes in

the macroeconomic, regulatory, and competitive environments.1

Despite the rising importance of fee-based income as a proportion of total income for

many banks, net interest margins (NIM) remain one of the principal elements of bank net cash

flows and after-tax earnings.2 As shown in figure 1, except for very large institutions and credit

card specialists, noninterest income still remains a relatively small and usually more stable

component of bank earnings. As a result, despite earnings diversification, variations in net

interest income remain a key determinant of changes in profitability for a majority of banks.

However, research in the area of bank interest-rate risk and the behavior of NIM has been largely

limited since the late 1980s, when the savings and loan crisis brought the issue of interest-rate

risk to the fore. Understanding the systematic effects of changes in interest-rate and credit risks

on bank NIM will likely help the FDIC better prepare for variations in its contingent liability

associated with adverse developments in the macroeconomic and financial market environment.

1 For example, Duan et al. (1995) posit that interest-rate risk dominated the volatility of the FDIC’s contingent liabilities in the early 1980s—the time of high interest-rate volatility—whereas credit risk became the leading factor in the late 1980s and early 1990s, as interest-rate volatility subsided. 2 Throughout this paper, net interest margins are defined as annualized quarterly net interest income (interest income less interest expense) as a ratio of average earning assets.

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The objective of this paper is twofold. First, this paper develops a new dynamic model of

bank NIM that reflects the managerial decision process in response to credit, interest, and term-

structure shocks. We focus our analysis primarily on variations in net interest margins, although

bank managers adjust their portfolios in order to manage reported after-tax profit rather than net

interest margins. However, given that the variation in net interest income is the key determinant

of earnings volatility for many banks, understanding the degree to which these shocks affect the

bank’s net interest income would help us identify the channels through which they could affect

overall bank profitability and the responses bankers make to manage reported profitability. The

degree to which the bank can change the portfolio mix and/or hedge in the short term would

determine the magnitude of the effect of interest-rate changes and other shocks on bank

profitability.

Our second objective is to use a large set of data, consisting of quarterly bank and

financial market data from first quarter 1986 to second quarter 2003, to evaluate the model. In

addition, we investigate whether the sensitivity to shocks varies across diverse bank groups on

the basis of their product-line specializations as well as different regulatory regimes. We focus

on the effects of three key legislative changes on bank NIM during the sample period: the

Depository Institutions Deregulation and Monetary Control Act (DIDMCA) of 1980, which set

in motion the phasing out of the Regulation Q ceilings on deposits; the Federal Deposit

Insurance Corporation Improvement Act (FDICIA) of 1991; and the Riegle-Neal Interstate

Banking and Branching Efficiency Act (Riegle-Neal) of 1994, which became effective in July

1997.3 These pieces of legislation have likely changed the sensitivity of bank NIM to credit,

interest-rate, and term-structure shocks, for they spurred price competition for deposits that

3 See FDIC (1997) for a detailed discussion of the legislative and regulatory history of the banking crisis of the 1980s and early 1990s.

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reduced volatility in bank lending, improved the capital positions of banks, allowed geographic

and earnings diversification, and changed the general competitive landscape. No empirical study

to date has investigated the effects of these legislative changes on the behavior of bank NIM.

Empirical evidence and casual observation reinforce the view that banks with different

product-line specializations tend to have distinctive business models and corresponding risk-

management practices and characteristics. In addition, banks with different product-line

specializations also face different competitive landscapes, with some bank groups experiencing

progressively more intense competition than others. To maximize profitability and enhance bank

value, bankers attempt to choose a product mix that best fits their perceived markets and

managerial expertise, thus gaining a competitive advantage for lending, investing, and raising

funds through deposits. For most banks, the choice of market means some degree of

specialization in particular product lines and geographic locations. The bank portfolios

associated with these various product lines are likely to exhibit different degrees of sensitivity to

interest-rate and credit-risk changes. The extent to which bankers can offset adverse interest-rate

changes and hedge adverse credit-risk changes will depend on the principal product line of the

bank, the flexibility of the portfolio in responding to change, and the cost and availability of

hedges for a particular portfolio.

Our empirical results show that net interest margins associated with some bank portfolios

derived from specializing in certain product lines are considerably more sensitive to interest-rate

changes than others. The magnitude of these effects depends on the repricing composition of

existing assets and liabilities: banks that have a higher proportion of net short-term assets in their

portfolio experience a greater boost in their NIM as interest rates rise. We find that changes in

bank net interest margins are typically negatively related to interest-rate volatility but positively

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related to increases in the slope of the yield curve. Changes in the yield spread have significant

and lingering effects on NIM for many bank groups, but the effects are particularly notable for

mortgage specialists and small community banks. We find that, for most bank groups, after-tax

earnings are less sensitive to interest-rate changes than NIM are, but the degree of sensitivity

differs among banks with different product-line specialties.

We find that bank NIM are negatively related to an increase in realized and expected

credit losses, particularly among banks specializing in commercial-type loans (i.e., commercial

and industrial loans and commercial real estate loans). We posit that this inverse relationship

between realized credit risk, as indicated by an increase in nonperforming loans, and net interest

margins exists because, in the short run, risk-averse bank managers reallocate their funds to less

default-risky, lower-yielding assets in response to an increase in the credit risk of their portfolios.

This response is reinforced by bank examiners, who encourage banks to reduce their exposure to

risky credits when loan quality is observed to be deteriorating. Banks’ net interest margins are

positively related to a size-preserving increase in high-yielding, and presumably higher-risk,

loans. We generally find that the estimated parameters of the models differ by subperiod for

banks with different product-line specialties in ways that are statistically and economically

meaningful.

This paper extends the existing literature on NIM in three important respects. First, we

develop a dynamic behavioral model of variations in NIM in response to market shocks that

more closely resembles the actual decision-making process of bank managers than existing

models. Second, by treating the banking industry as inherently heterogeneous (which we do by

dividing banks into groups based on their product-line specializations), we are able to proxy

broad differences in business models and managerial practices within the banking industry, and

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identify groups of banks that are most sensitive to credit, interest-rate, and/or term-structure

shocks. Finally, we are able to test the importance of shifts in regulatory regime in behavioral

differences across subperiods for the same group of banks.

The rest of the paper is organized as follows: section 2 reviews the literature relating to

interest effects on bank net interest margins; section 3 presents a theoretical model of bank

behavior in response to interest-rate shocks; section 4 discusses the data, the empirical variables,

and the empirical specifications for the model; section 5 presents the results of both the full

sample period and the subsample periods; and section 6 concludes the paper.

2. Literature Review

Despite significant regulatory concern paid to the interest-rate risk that banks face (OCC

[2004]; Basel Committee on Banking Supervision [2004]), research on a key component of

earnings that may be most sensitive to interest shocks—namely, bank net interest margins—has

been limited thus far, particularly for U.S. banks. With a few exceptions discussed in this

section, there has been little published research on the effects of interest-rate risk on bank

performance since the late 1980s. Theoretical models of net interest margins have typically

derived an optimal margin for a bank, given the uncertainty, the competitive structure of the

market in which it operates, and the degree of its management’s risk aversion. The fundamental

assumption of bank behavior in these models is that the net interest margin is an objective to be

maximized. In the dealer model developed by Ho and Saunders (1981), bank uncertainty results

from an asynchronous and random arrival of loans and deposits. A banking firm that maximizes

the utility of shareholder wealth selects an optimal markup (markdown) for loans (deposits) that

minimizes the risks of surplus in the demand for deposits or in the supply of loans. Ho and

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Saunders control for idiosyncratic factors that influence the net interest margins of an individual

bank, and derive a “pure interest margin,” which is assumed to be universal across banks. They

find that this “pure interest margin” depends on the degree of management risk aversion, the size

of bank transactions, the banking market structure, and interest-rate volatility, with the rate

volatility dominating the change in the pure interest margin over time.

Allen (1988) extends the single-product model of Ho and Saunders to include

heterogeneous loans and deposits, and posits that pure interest spreads may be reduced as a result

of product diversification. Saunders and Schumacher (2000) apply the dealer model to six

European countries and the United States, using data for 614 banks for the period from 1988 to

1995, and find that regulatory requirements and interest-rate volatility have significant effects on

bank interest-rate margins across these countries.

Angbazo (1997) develops an empirical model, using Call Report data for different size

classes of banks for the period between 1989 and 1993, incorporating credit risk into the basic

NIM model, and finds that the net interest margins of commercial banks reflect both default and

interest-rate risk premia and that banks of different sizes are sensitive to different types of risk.

Angbazo finds that among commercial banks with assets greater than $1 billion, net interest

margins of money-center banks are sensitive to credit risk but not to interest-rate risk, whereas

the NIM of regional banks are sensitive to interest-rate risk but not to credit risk. In addition,

Angbazo finds that off-balance-sheet items do affect net interest margins for all bank types

except regional banks. Individual off-balance-sheet items such as loan commitments, letters of

credit, net securities lent, net acceptances acquired, swaps, and options have varying degrees of

statistical significance across bank types.

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Zarruk (1989) presents an alternative theoretical model of net interest margins for a

banking firm that maximizes an expected utility of profits that relies on the “cost of goods sold”

approach. Uncertainty is introduced to the model through the deposit supply function that

contains a random element.4 Zarruk posits that under a reasonable assumption of decreasing

absolute risk aversion, the bank’s spread increases with the amount of equity capital and

decreases with deposit variability. Risk-averse firms lower the risk of profit variability by

increasing the deposit rate. Zarruk and Madura (1992) show that when uncertainty arises from

loan losses, deposit insurance, and capital regulations, a higher uncertainty of loan losses will

have a negative effect on net interest margins. Madura and Zarruk (1995) find that bank interest-

rate risk varies among countries, a finding that supports the need to capture interest-rate risk

differentials in the risk-based capital requirements. However, Wong (1997) introduces multiple

sources of uncertainty to the model and finds that size-preserving increases in the bank’s market

power, an increase in the marginal administrative cost of loans, and mean-preserving increases in

credit risk and interest-rate risk have positive effects on the bank spread.

Both the dealer and cost-of-goods models of net interest margins have two important

limitations. First, these models are single-horizon, static models in which homogenous assets

and liabilities are priced at prevailing loan and deposit rates on the basis of the same reference

rate. In reality, bank portfolios are characterized by heterogeneous assets and liabilities that have

different security, maturity, and repricing structures that often extend far beyond a single

horizon. As a result, assuming that bankers do not have perfect foresight, decisions regarding

loans and deposits made in one period affect net interest margins in subsequent periods as banks

face changes in interest-rate volatility, the yield curve, and credit risk. Banks’ ability to respond

4 Uncertainty in the bank’s deposit supply function is modeled as D* = D(RD ) + µ where RD is the interest rate on deposits and µ is a random term with a known probability density function.

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to these shocks in the period t is constrained by the ex ante composition of their assets and

liabilities and their capacity to price changes in risks effectively. In addition, the credit cycle and

the strength of new loan demand determine the magnitude of the effect of interest-rate shocks on

banks’ earnings. In this regard, Hasan and Sarkar (2002) show that banks with a larger lending

slack, or a greater amount of “loans-in-process,” are less vulnerable to interest-rate risk than

banks with a smaller amount of loans in process. Empirical evidence, using aggregate bank loan

and time deposit (CD) data from 1985 to 1996, indicates that low-slack banks indeed have

significantly more interest-rate risk than high-slack banks. The model also makes predictions

regarding the effect of deposit and lending rate parameters on bank credit availability that were

not empirically tested with aggregate data.

The second important limitation of both the dealer and cost-of-goods models of net

interest margins is that they treat the banking industry either as being homogenous or as having

limited heterogeneous traits based only on their asset size. However, banks with distinct

production-line specializations usually differ in terms of their business models, pricing power,

and funding structure, all of which likely affect net interest margin sensitivity to interest-rate and

other shocks. For instance, in the 1980s and early 1990s, credit card interest rates were typically

viewed as “sticky” or insensitive to market rates, a view suggesting imperfect market

competition (Ausubel [1991]; Calem and Mester [1995]). This view would imply that net

interest margins of credit card banks, as a group, would be significantly less sensitive to interest-

rate shocks than other banks. Furletti (2003) documents notable changes in credit card pricing

due to intense competition over the past decade; however, it is not clear how these changes have

affected credit card specialists’ sensitivity to interest-rate and other shocks. In comparison,

mortgage lenders, as a group, have a balance sheet with a significant mismatch in the maturity of

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their assets and liabilities, and they are therefore more likely to be sensitive to changes in the

yield curve.

3. A Model of Bank Behavior

Discussed in this section is a model of the effects of interest-rate and credit risk changes

using the mismatching of asset and liability repricing frequencies. The model is a standard

approach to evaluating changes in NIM due to changes in interest rates and credit quality as

loans that are passed-due or charged off are essentially repriced in the current period.

3.1 Interest-Rate Changes

The model of bank behavior relating to net interest margins used in this paper assumes

that at each period a bank can significantly but not completely choose the amount of its

investment in assets and liabilities of different repricing frequencies, given past choices that are

immutable. Admittedly, this is a fuzzy statement as to the choices available to a bank, but banks

have a moderate degree of control over their asset mix in the short run (from quarter to quarter)

by purchasing or selling assets of different repricing frequencies. As suggested above, banks’

choices of principal product-line specializations will determine the market conditions they face

that may limit their ability to make rapid asset portfolio adjustments. The same is true for bank

liabilities. Bankers can pay them early, deposits can be received and withdrawn at random, and

some of them, like federal funds and repurchase agreements, are under the control of the bank

and can be changed overnight.

In contrast to banks’ ability to make portfolio adjustments, banks have little control over

market interest-rate changes and interest-rate volatility. When contracts on assets or liabilities

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are negotiated, banks may, through market power, be able to set levels or markups (markdowns)

over index rates such as LIBOR, but are unable to control index rate changes. In addition, we

assume that markups are contractually fixed in the short run. Furthermore, banks are unable to

change their chosen product-line specializations in the short run, so such changes are strategic

options only.

In our modeling of bank responses to credit and interest-rate risks, we assume that banks

are most interested in achieving the best after-tax profit performance they can in order to provide

shareholders with maximum value. Maximizing shareholder value in a dynamic context,

however, is a daunting problem and requires considerable judgment. Not only do bank managers

have to choose the optimal financial service product mix (product-line specialization, in this

study) and geographic diversification, but they also need to set the lending rate and fees, hedge

credit quality and volatility changes, manage their liability structure, and gauge the moods of the

equity and debt markets to favorable or unfavorable news so as to increase or protect shareholder

value. Given these underlying conditions regarding banks’ motivations and their ability to

change their portfolios and their positions as interest-rate takers, we assume that banks operate

such that they will change their portfolio mix only to increase profits and maximize shareholder

value over a 12-month horizon. As discussed above, the net interest margin is the major source

of net income for most banks, and therefore a strategy of maximizing its value in the short run

may be a reasonable proximate goal for achieving maximum bank profits in the short run. If

risk-neutral pricing were prevalent in financial markets, banks would all price loans in a similar

way, and short-run maximization of the expected value of net interest margins would be a proper

bank objective.5 However, banks can do better. They can make decisions as to the timing of

5 As pointed out in the introduction, banks in general have been increasing fee income as a way to achieve greater long-run profitability. Fee income is difficult to adjust in the short run in response to interest-rate changes because

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credit charge-offs, changing portfolios for credit risk purposes, and changing asset structure by

buying or selling liquid assets (U.S. government and agency debt).

To best consider the interest-rate sensitivity of net interest margin, we consider the net

interest margin as a function of interest rates on assets and liabilities and the shares of each as a

ratio to earning assets at each repricing frequency. Throughout the development of the model,

we are assuming that the bank has chosen its product-line specialization and that the assets and

liabilities reflect this choice for each bank. This relationship can be formally stated as

EA

⎛⎜ ⎝

⎞⎟ ⎠

m

k 1

where p refers to product line p, NIMpt is net interest margin in t, NIIt is net interest income

(interest income less interest expense) in t, EApt is the amount of interest-earning assets in the

∑=

portfolio in t, yk is the interest rate on assets of repricing frequency k, EAk is the amount of

earning assets in repricing frequency k, rk is the interest rate on liabilities for repricing frequency

k, and Lk is the amount of liabilities for repricing frequency k. Operationally, the first repricing

frequency, for example, would be overnight.

Since NIM will be subject to changes in interest rates on earning assets and interest-

bearing liabilities, changes in individual investments in earning assets, funding from interest-

bearing liabilities and changes in the overall investment in earning assets, the continuous change

in NIM, dNIM, is a function of these bank management portfolio decisions and of time. In

general, this can be expressed more formally, assuming continuous time and using (1) for any

product line, as follows:

y EAkt kt − r Lkt kt pNII pt EANIM (1) = = pt pt pt

of its longer-term contractual basis. One exception is for credit card banks, where fees can be modified at the will of the lender, as can interest rates on outstanding balances of accumulated interest and original principal.

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∂NIM ∂NIM dNII NIIt t t tdNIM = dNII + dEA = − dEA (2)t t t 2 t∂NII ∂EA EA EAt t t t

where the changes in NII and EA, dNII and dEA, are the result of changes in the interest rates, dyk

and drk and bank management decisions on investments in EA. The product-line index is

dropped to simplify the notation.

Noting that the total derivative of NII can be expanded in terms of interest-rate, earning

asset, and liability changes:

m m∂NII t ∂NIItdNII t = ∑ dyk − drk = ∑ EAk dyk + yk dEAk − Lk drk − rk dLk (3) k =1 ∂yk ∂rk k =1

In this formulation, we assume that interest-rate changes are independent of each other, which is

not usually the case. We can change this assumption by substituting a term-structure and credit-

risk spread factor model for each interest-rate change. For the NIM modeling, we will use a

more simplified approach that can accommodate the term-structure and credit-risk spread effects

on NIM.

Expressing the interest change effects on NIM, we substitute (3) into (2) for dNII

resulting in

⎛ m ⎞⎜∑EA dyk + y dEA − L dr − r dL ⎟k k k k k k k⎝ k =1 ⎠ dEAtdNIM t = − NIM t (4)EAt EAt

Note that the final term in (4) is the proportional change in EA over the preceding period times

the current period NIM. This term is negatively related to the change in NIM, implying that if all

other factors are held constant, increases in earning assets will tend to decrease the net interest

margin. With respect to the first term in (4), constant interest rates mean that all dyk and drk are

zero such that the proportion of each asset and liability component relative to EAt would have no

effect on the change in NIM. Under these ceteris paribus conditions, this term is the ratio of the

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change in NII resulting from a change in each asset and liability component, with each

component’s proportion to EA held constant. If dEAt is positive and each dEAk and dLk grows at

the same positive rate as earning assets, the effect would be to increase NII such that dNII was

positive as long as NIMt was positive. The net effect on NIM under these conditions is zero.

The implication of this result is important for interpreting the effect of the growth in

earning assets on banks' net interest margins. Without advantageous changes in interest rates or

changes in the composition of assets and liabilities relative to earning assets, a growth in earning

assets will have little effect on NIM. Banks should experience an increase in NII by practically

the same proportion as EA. Therefore, management cannot rely solely on growth to increase

NIM or profitability but must manage the composition of assets and liabilities to achieve greater

NIM and ROA, given management’s expectation of changes in interest rates and term structure.

To complete the model for estimation, changes in interest rates are assumed to be outside

the control of management and each is subject to a continuous time, stochastic diffusion process

as follows:

dyk = f (yk , t)dt +σ y dzk (5) k

where σyk is the standard deviation of changes in yk, f(yk,t) is a drift term or mean for dyk, and dzk

is a Weiner process of interest-rate changes with repricing frequency k. We assume, for

simplicity, that each yk and rk follows the same stochastic processes so that dz depends only on

the repricing frequency, k. Furthermore, the drift term requires a hypothesis for its value. If it is

hypothesized that there is a tendency of regression toward a mean (e.g., Vasicek and Heath-

Jarrow-Morton models), the sign of the term will depend on whether interest rates are above or

below the mean. Another hypothesis is that the drift term is zero because interest rates follow a

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random walk once regime shifts are complete (see Ingersoll [1987], 403).6 Since we do not wish

to impose an interest-rate adjustment hypothesis or a term-structure hypothesis on bankers’

adjustment to interest-rate changes, we will allow the data to provide estimates of the effect of

interest-rate and term-structure changes.7 These interest-rate diffusion processes can be

substituted into (4) for the final model:

⎛ m ⎞⎜∑ EAk f (yk , t) + EAkσ y dzk + yk dEAk − Lk f (rk , t)− Lkσ r dzk − rk dLk ⎟ ⎝ k =1 k k ⎠ dEAtdNIM t = − NIM tEAt EAt

(6)

The drift terms, f(yk,t) and f(rk,t), pose an interesting way of viewing the sign of any estimation of

the coefficient on EAk or Lk. If these terms are zero and E(dzk) is zero, the effect of changes in

earning assets is strictly conditioned by interest rate changes.

If interest rates increase for assets and liabilities with repricing frequencies of less than

one year, the change in NIM, all other factors held constant, depends on the relative shares of

earning assets and liabilities repricing within one year. If short-term liabilities have a greater

proportion of EAt than assets, dNIM will be negative and NIM will fall in the next period. Note

also that the effect of interest-rate volatility on NIM, σyk and σrk, will be in the same direction as

respective interest-rate changes, meaning that higher interest volatility has the same relationship

as an increase in interest rates depending on the sign of the repricing gap, the difference between

assets and liabilities in the same repricing frequency, or cumulative repricing frequencies.

6 The hypothesis of a random walk is perhaps most appropriate for the period under analysis. From 1984 to the present, there have been several regime shifts in interest-rate levels due to the substantial and sustained decline of inflation and shifts in monetary policy. The purpose of our study is not to explain these shifts but to allow the data to provide parameter estimates of bankers’ responses to interest-rate changes. 7 In dealing with data on a quarterly frequency, we considered the imposition of the unbiased expectations hypothesis on interest-rate changes and the conjoint assumption of risk-neutral pricing to be a second-order constraint for the purposes of this study. The focus of this study is to estimate bankers’ reactions to prior interest-rate, term-structure, and volatility changes and not to impose a particular model. The unbiased expectations hypothesis will be used to help interpret the estimated coefficients, since the pricing that results is risk neutral.

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Furthermore, the change in NIM is inversely related to the level of prior-period NIM and, since

NIMt is always positive, to the rate of change in EA, ceteris paribus. Since the rate of change in

EA can be positive or negative, its sign must be accounted for in estimations.

By way of comparison, another approach to modeling changes in NIM is to use Ito’s

lemma by assuming that the change in NIM follows a diffusion process as below:

m m m m 2⎛ ∂NIM ∂NII ∂NIM ∂NII ⎞ ∂NIM 1 ∂ NIMt t t t t tdNIM t = ⎜∑ dyk −∑ drk ⎟⎟ + dt + ∑∑σ ij (7)⎜⎝ k =1 ∂NIIt ∂yk k =1 ∂NIIt ∂rk ⎠ ∂t 2 i=1 j=1 ∂xi ∂x j

where all variables are as described above, xi and xj are interest rates composed of y and r and

stated this way in (7) for simplicity, and σij is the covariance among all interest-rate changes of

assets, dy, and liabilities, dr. To expand (7), note that the terms in parentheses are equivalent to

equation (4), where earning assets are allowed to change. The middle term in (7) is the drift of

NIM over time and can be thought of as a trend in NIM. When the diffusion process for interest

rates is substituted from (5) into (7), the term in parentheses is equivalent to (6). This approach

adds the drift and the second-order stochastic term within the double sum in (7). This final term

can be interpreted as the portfolio effect on dNIMt due to interest-rate volatility and correlation—

a portfolio risk effect. If interest rates are positively correlated within most interest-rate regimes

(see Hanweck and Hanweck [1995]; Hanweck and Shull [1996]), the σij are positive and the sign

of the double-sum term will depend on the sign of the second derivative of NIM with respect to

interest rates. This term could be positive or negative depending on whether the interest rates are

only for assets or only for liabilities. For asset terms the sign is negative; for asset and liability

terms the sign depends on the weight of assets and liabilities at each repricing period and is

likely to be negative for one-year repricing items; and for all liabilities the sign is likely to be

positive. With positive correlations of interest-rate changes, we expect the weight of the terms to

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be such that changes in volatility will be negatively related to the change in NIM for most banks

regardless of product-line specialization. This result is consistent with the hypothesis expressed

in equation (6), but with the correlations of interest-rate changes added. Thus, this approach

reinforces the role of interest volatility for changes in NIM.

This form of a model of NIM change is much less theoretically appealing because it

assumes that earning assets and liabilities are almost exclusively stochastic, similar to the

assumption of Ho and Saunders (1981), when it is well known that banks can and do change the

distribution of assets and liabilities among their repricing buckets substantially from quarter to

quarter for strategic purposes, presumably to take advantage of expected future interest-rate

changes (see Saunders and Cornett [2003], chap. 9, for this evidence). Thus, we focus our

empirical work using the model represented by (6) while taking advantage of the insights of the

second model regarding interest-rate volatility and correlation by maturity and risk class.

3.2 Credit Risk

Some important factors influencing changes in NIM have been left out of the models

above in order to achieve simplicity in focusing on interest-rate change effects on NIM. One

important factor, as pointed out by Zarruk and Madura (1992), Angbazo (1997), and Wong

(1997), is the effect of credit risk or risk of loan losses on NIM. Angbazo and Wong

hypothesized that NIM should be positively related to loan losses, arguing that greater credit risk

would mean that banks would charge higher premiums. An implication of this hypothesis is that

expected increases in credit risk would prompt banks to raise interest-rate markups on the basis

of these perceived future loan losses. Although it may be the case in the long run that greater

credit risk will lead to higher NIM through the pricing of risk, quarterly or short-run changes in

18

the NIM are more likely to respond inversely to increases in credit risk. Like Zarruk and

Madura, we argue that when faced with higher uncertainty of loan losses—that is, an increase in

credit risk of their portfolios—risk-averse bank managers will shift funds to less default-risky,

lower-yielding assets over the short-term horizon. In addition, bank examiners will put pressure

on banks to reduce their exposure to risky credits when loan quality starts to deteriorate. These

supervisory actions imply that a deterioration in loan quality, indicated by rising loan losses or

nonperforming loans relative to earning assets, causes banks to lose interest income from these

loans and move funds to less default-risky, lower-yielding assets. Both effects tend to decrease

NIM in the short run, so that decreases in credit quality tend to decrease NIM.

We can integrate these concepts directly into the above model by using equation (6). The

total change in NIM, dNIMt, now becomes a function of interest-rate changes and credit-quality

changes. We can incorporate credit quality by defining the value of an earning asset as

composed of two components: the promised value, less the value of an option held by the bank

(the lender) to take over the assets of the borrower if the loan is not paid off on time and in full.8

An increase in the value of this option means that the credit quality of the borrower has

decreased and the bank’s credit risk has increased. This relationship is shown more formally as

EA = BEA − P (A , BEA ,T , Rf ) (8) k k t b k k

where EAk is the market value of the earning asset of repricing frequency k, BEAk is the

promised value of the debt, Pt() is the put option on the assets of the firm, Ab, T is the time to

repricing, and Rfk is the value of the default risk-free rate for repricing frequency k. Since the

8 See Black and Cox (1976); Merton (1974); and Cox and Rubenstein (1985), 378–80 for the structural models for debt valuation. Conceptually, the value of the shareholders’ interest can be thought of as a call option on the assets of the firm, with the ability to put the assets to the debt holders if the value of the assets is less than the promised value of the debt. Thus debt holders, lenders such as banks, have a short put option on the firm’s assets with a strike price of the promised value of the debt.

19

book value of interest-earning assets is approximately equal to the promised value, we can

substitute EAk in equation (6) with equation (8) to arrive at the following relationship:

⎛ ⎞⎜∑

m

(BEAk − Pt ()) f (yk , t)+ (BEAk − Pt ())σ y dzk + yk d (BEAk − p()) − Lk f (rk , t)− Lk σ r dzk − rk dLk ⎟ ⎝ k =1 k k ⎠dNIM t = (BEAk − Pt ())

d (BEAt − Pt ())− NIM t (BEAt − Pt ()) (9)

Since the promised value of the debt is fixed, the value of the put option directly reflects changes

in credit risk. An increase in the value of the put option means that the put is closer to being in

the money and default is more likely. By considering these factors, we see that the change in

NIM is inversely related to increases in credit risk.

We can evaluate the effect of interest-rate changes on default-risky debt by using

equation (8). An increase in the base interest-rate index will reduce the promised value, BEAk,

by increasing the discount factor. However, a rise in interest rates will also reduce the value of

the put option because the present value of the strike price (the promised value) is reduced. The

reduction implies that default-risky debt is less sensitive to a given change in the interest-rate

index than default-free debt. If default risk is independent of interest-rate changes, bank

specializing in higher credit-risk lending should be less interest sensitive than banks with

concentrations in default-risky debt.

4. Data and the Empirical Model

In this section we describe the data, the empirical variables (for interest-rate shock, for

term-structure shock, for credit shock, other institutional variables, and for seasonality), and our

empirical specifications.

20

4.1 Data

We obtained individual bank data for the estimation of these models from the Reports of

Condition and Income (Call Reports) collected on a quarterly basis by the FDIC from the first

quarter of 1986 to the second quarter of 2003. Data for financial market variables are from

Haver Analytics and the Federal Reserve Board of Governors. Because of issues related to data

consistency and availability, BIF-insured thrifts and Thrift Financial Report filers are excluded

from the sample. Although available, bank data before the first quarter of 1986 were excluded

from the sample because of the existence of Regulation Q, which constrained banks’ ability to

adjust interest rates on deposits in response to changes in market interest rates.9 To exclude

spurious financial ratios, we restricted the sample to commercial banks with earning assets of $1

million or more and a ratio of earning assets to total assets exceeding 30 percent. This left

22,077 commercial bank observations in the sample of banks that were in existence for one or

more quarters over the sample period. We also excluded any observation with missing data

points, reducing the sample to 17,789 commercial banks.

We then divided the sample into 12 different bank groups based on the specialization and

asset size of the bank at the end of each quarter. These bank groups practically correspond to the

classification method used by the FDIC to identify a specialty peer group of insured institutions

except that we make three main alterations to the FDIC peer grouping to better reflect

differences in the institutions’ risk characteristics. First, we break down “commercial lenders”

more finely to better reflect differences in risk characteristics between commercial and industrial

(C&I) loan and commercial real estate (CRE) loan portfolios. Second, we separate consider

noninternational banks with assets over $10 billion to account for potentially greater reliance on

hedging activities that may offset the adverse effects of interest-rate shocks. Finally, to be able

9 The final phasing out of Regulation Q occurred in the second quarter of 1986.

21

to compare asset size over time, we use real assets rather than nominal assets to classify bank

size groups.10 This classification method helps stratify commercial banks on the basis of their

business models, portfolio compositions, and risk characteristics. Given dissimilarities in their

risk characteristics, we expect banks in these different groups to exhibit varying degrees of

sensitivity to credit, interest-rate, and term-structure shocks. We also considered a classification

method based on derivative activities; however, data on derivatives are severely limited,

particularly for the full sample period, so it would be difficult to assess the extent to which

commercial banks use derivatives for hedging purposes. We use asset size as a proxy to identify

groups of banks most likely to use derivatives to hedge their interest-rate risk.

The 12 bank groups are

• International banks

• Large noninternational banks with real assets over $10 billion

• Agricultural banks

• Credit card banks

• Commercial and industrial (C&I) loan specialists

• Commercial real estate (CRE) specialists

• Commercial loan specialists

• Mortgage specialists

• Consumer loan specialists

• Other small specialists with real assets of $1 billion or less

• Nonspecialist banks with real assets of $1 billion or less

• Nonspecialist banks with real assets between $1 billion and $10 billion.

10 To compute real assets, we divided nominal assets by the CPI-U price-level index for the quarter.

22

http:groups.10

Because of the size and diversity of the group of commercial loan specialists and the

grouop of small nonspecialists, each is further broken down into three groups on the basis of the

size of their real assets. Appendix 1 describes the criteria for each of these bank groups. Each

bank is classified in 1 of the 12 groups in a given quarter, but it may belong to 2 or more bank

groups throughout the sample period as the bank changes its asset composition or its business

model or both. For each bank group, we eliminated any bank that did not belong to the group for

at least four quarters, thus making the final sample 16,522 commercial banks.

The Call Reports require banks to report cumulative year-to-date income and expenses on

a quarterly basis. Reflecting this reporting standard, most studies and quarterly reports by the

FDIC and Federal Reserve of bank performance report NIM as an annualized, cumulative value

(see the FDIC release of the Quarterly Bank Performance Report at www.FDIC.gov). The use of

quarterly cumulative reports tends to smooth changes in NIM, reducing actual quarterly

variations. To overcome this problem, we focus on quarterly changes in the net interest margin.

For the second quarter through the fourth quarter of each year, we estimate actual income and

expenses for the quarter by subtracting the previous quarter’s cumulative reported values from

the current cumulative reported values. For the first quarter, we use reported income and

expenses for the quarter. We then annualize these values by multiplying each by four. We

compared the resulting series with the cumulative series in model estimation and found that the

resulting series’ performance was much more consistent with the hypothesized behavior.

Therefore, all income and expense derived data are based on adjusted series. The reported

earning assets—the denominator of computed ratios—are the average of ending values for the

quarter and the previous quarter.

23

http:www.FDIC.gov

Nine panels in figure 1 show trends in net interest margins and noninterest income for

each of our 12 bank groups. These panels show a long-term trend of a decline in net interest

margins for most bank types, beginning around the 1992–1993 period. In particular,

international banks have experienced a significant compression in their net interest margins since

the early 1990s, with the median net interest margin for the group falling by more than 175 basis

points. It is not clear how much of this long-term decline can be attributed to the low interest-

rate environment, greater competitive pressure, or regulatory changes that made securitization

and other off-balance-sheet activities more attractive. However, it is interesting to note that the

peak year in net interest margins roughly corresponds to the implementation of capital regulation

rules and prompt corrective action as specified in FDICIA.

Aggregate industry statistics show a growing importance of noninterest income as a

source of bank earnings. The FDIC Quarterly Banking Profile shows that noninterest income

rose from 31 percent of quarterly net operating revenue in first quarter 1995 to 41 percent in

second quarter 2003. However, most bank groups did not experience a notable increase in

noninterest income as a percentage of average earning assets over most of the sample period. In

fact, the median quarterly noninterest income as a percentage of average earning assets remained

mostly stable for most bank groups throughout the 1990s. DeYoung and Rice (2004) suggest

that the long-term increase in noninterest income may have already peaked as the risk-return

trade-off reached a plateau.

International banks, large banks with real assets exceeding $10 billion, and credit card

specialists did experience a sharp increase in noninterest income over the sample period. The

median ratio of noninterest income to average earning assets for the international bank group

rose sharply after 1997, overtaking net interest margins as the primary source of this grooup’s

24

earnings. This trend likely reflects earnings and product diversification and a greater reliance on

off-balance-sheet instruments by these banks in response to deregulation, capital regulation, and

financial market developments.11 Rogers and Sinkey (1999) found that banks that are larger and

have smaller net interest margins and fewer core deposits, as is the case of international banks,

tend to engage more heavily in nontraditional activities.

As figure 1 shows, large banks with real assets greater than $10 billion saw their

noninterest income rise steadily, although net interest income still represents their primary source

of earnings. The net interest margin fluctuated between 3.5 percent and 4.5 percent of average

earning assets for this group of banks. Unlike for other bank groups, for credit card specialists

the median net interest margins did not exhibit a discernible downward trend in the 1990s. The

median net interest margin for credit card banks increased sharply in the 2001–2003 period

despite a steady decline in short-term interest rates. At the same time, the median noninterest

income for the group has risen sharply since 1997. This trend likely reflects a widespread use of

risk-based pricing and risk-related fees in response to heightened rate competition and greater

availability of credit card loans to higher-risk and higher-revenue-generating borrowers than

previously.12

Figure 2 presents the median quarterly return on average earning assets (ROA) for

selected groups of banks. The median ROA for large and midtier banks has improved

significantly since the implementation of FDICIA, and it has remained more stable since then

compared with prior periods. Between 2002 and 2003, however, large banks with real assets

greater than $10 billion saw their ROA rising sharply, whereas international and midtier

11 See Angbazo (1997) for the effects of off-balance-sheet instruments on net interest margins. Angbazo found a negative relationship between letters of credit, net securities lent, and net acceptances acquired and net interest margins, but a positive relationship between net loans originated/sold and net interest margins. 12 See Furletti (2003) for discussions of recent developments in credit card pricing and fee income.

25

http:previously.12http:developments.11

nonspecialists reported weaker earnings. These differing trends suggest diversity across these

three largest asset size groups in their business models in terms of asset composition, correlation

among earning components, and earnings management. The earnings volatility of international

banks suggests that they are vulnerable to market factors other than those included in our model;

however, discussion on the effect of these factors on bank earnings is outside the scope of this

paper. As for large banks, the median ROA for small nonspecialist banks made discrete

improvements in 1992. The ROA of these banks, particularly the smallest asset size group, has

exhibited a high degree of seasonality over time.

4.2 Empirical Variables

Appendix 2 lists the explanatory variables included in our empirical model and their

expected signs. All variables representing financial ratios or interest rates are expressed in

annualized percentage terms. Bank-specific variables and financial market variables included in

the empirical model are derived from the theoretical model of bank behavior presented in section

3 of this paper. Table 1 presents descriptive statistics for bank-specific variables for each bank

group. To preserve earnings data for an individual institution at a given time, we did not adjust

the bank data for mergers and acquisitions that occurred over the sample period. Instead, we

screened the sample for any aberrant data on an individual-bank basis. As discussed below,

there exist significant variations in the value of each of these bank-specific variables across bank

groups as well as within the given bank group.

4.2.1 Interest-Rate-Shock Variables

26

VOL_1Y represents short-term interest-rate volatility and is measured by the standard

deviation of a weekly series of one-year Treasury yields for the quarter. ST_DUMMY is a

dummy variable that takes a value of one if the one-year Treasury yield rose during the quarter,

and zero if the yield fell. Figure 4 illustrates a mostly positive but imperfect correlation between

the quarterly short-term interest-rate volatility and the level of short-term interest rates. Equation

(7) posits that the coefficients for both VOL_1Y and ST_DUMMY would have a negative sign

for most banks.

The duration gap between assets and liabilities measures respective changes in assets and

liabilities due to an interest-rate shock and is a key determinant of bank net interest margins

(Mays [1999]). The duration gap reflects the repricing frequency of assets and liabilities as well

as the value of embedded call options. Data necessary to calculate the duration gap are not

collected in the Call Report for commercial banks, so we are prevented from using a reported

duration gap in our empirical model. As a proxy for the interest-rate sensitivity of bank

portfolios, we use net short-term assets—the difference between short-term assets and short-term

liabilities. We define a repricing frequency less than one year as “short term.” STGAP_RAT is

net short-term assets as a percentage of earning assets. Although there have been changes in Call

Report data items and their definitions over time, we believe that STGAP_RAT is generally

comparable over time because many of these changes affected both assets and liabilities. Our

definition of STGAP_RAT includes nonmaturing liabilities that are discussed more fully below.

Table 1 shows that, whereas international banks and credit card specialists tend to have better

matched assets and liabilities than other bank groups, consumer loan specialists, mortgage

specialists, other small specialists, and small nonspecialist banks tend to have the most

unmatched balance sheets. Holding everything else constant, we expect the coefficient for

27

STGAP_RAT to have a negative sign since longer-term assets have higher yields than shorter-

term assets with the same risk characteristics. In addition, we expect the size of STGAP_RAT to

have a positive effect on NIM when short-term interest rates rise.

Flannery and James (1984) show that deposits with uncertain maturity, such as demand

deposits, regular savings accounts, and small time deposits, have an effective maturity longer

than one year. This finding suggests that the “effective” cost of these liabilities is relatively

insensitive to changes in market interest rates. Indeed, Mays (1999) found that thrifts with a high

percentage of nonmaturing deposits, defined as the sum of demand deposits and regular savings,

experienced a positive increase in net interest margins in response to a positive interest-rate

shock. Although these relationships may have changed in recent years as short-term interest

rates have reached 1.0 percent and less, we can test for any changes in this structure with models

estimated for different periods. We include NM_RAT, nonmaturing deposits as a percentage of

earning assets, in the model to proxy for the degree of interest-rate sensitivity of the bank’s

funding from nonmaturing deposits. As shown in table 1, commercial loan specialists and small

nonspecialist banks seem to rely most heavily on nonmaturing deposits to fund their lending,

whereas international and credit card banks fund their lending activities with more interest-rate-

sensitive liabilities. On the basis of previous studies, we expect the coefficient for NM_RAT to

have a positive sign. In addition, we expect the size of NM_RAT to have a marginal and

positive effect on NIM as interest rates rise, given the documented insensitivity of nonmaturing

liabilities to interest rate changes (Mays [1999]).

4.2.2 Term-Structure-Shock Variables

28

Figures 3 through 5 present historical trends in the financial market variables included in

our empirical model. DS5Y_1Y is the change in the spread between five-year and one-year

Treasury yields (yield spread). Given that maturities of bank assets are generally longer than

those of bank liabilities, we expect DS5Y_1Y to be positively related to DNIM_RAT. Figure 3

shows that the average DNIM_RAT for mortgage lenders has roughly tracked DS5Y_1Y over

time, although it seems to respond to the changing shape of the yield curve with one- or two-

quarter lags. A similar correlation exists between DNIM_RAT and DSY_1Y for other groups of

lenders, although visually the relationship is not as strong.

4.2.3 Credit-Shock Variables

DLN_AST and DCI_RAT are changes in, respectively, the ratio of loans to earning

assets and the ratio of C&I loans to earning assets from the prior quarter. Both variables proxy a

size-preserving increase in higher-yielding assets and are expected to be positively related to

DNIM_RAT. Table 1 shows that C&I specialists, CRE specialists, and credit card specialists

experienced the largest increases in median loan-to-asset ratios during the sample period,

whereas international banks, small other-specialty banks, and midtier nonspecialists reported the

largest declines. All bank subgroups other than C&I specialists experienced, on average, a

decline in C&I loan-to-asset ratios over the sample period.

We use the spread between the Baa corporate bond and the Aaa corporate bond yields

(CSPRD) to proxy for shocks in the credit market due to deterioration in credit quality or to other

credit market disturbances or to both, which may result in reduced liquidity in the market as well

as credit rationing. Among previous episodes of these credit events are the Mexican peso crisis

in 1995 and the Russian devaluation and default in August 1998 (the latter preceded the near

29

collapse of Long-Term Capital Management in the fall of 1998). In addition, as shown in figure

5, CSPRD is also closely related to the credit-risk premium measured by the spread between the

C&I loan rate and the intended federal funds rate. The relationship appears to have tightened in

the 1990s for C&I loans of all sizes, thus indicating that banks, both small and large, are better

able to price expected changes in credit risk. The coefficient for CSPRD is expected to have a

negative sign if banks are unable to increase loan rates but ration the supply of credit.

DNPERF_RAT is a change in the ratio of nonperforming assets to earning assets

(NPERF_RAT). This variable represents a change in realized credit losses, and is used as a

proxy for a “credit shock.” International banks, credit card specialists, and C&I specialists have

the highest median NPERF_RAT. The median value of DNPERF_RAT is close to zero;

however, there are some institutions within each group with large positive or negative values.

As discussed in section 3, the coefficient for DPERF_RAT is expected to have a negative sign if

banks are unable to price credit risk effectively in the short term, as bank managers shift funds to

lower-yielding assets.

4.2.4 Other Institutional Variables

Net interest margin (NIM_RAT) is annualized net interest income for the quarter divided

by average earnings assets. Table 1 shows that the median NIM_RAT varies significantly across

bank groups, with international banks having the lowest NIM_RAT on average (2.7 percent),

whereas while credit card specialists have the highest average NIM (9.3 percent). The median

DNIM_RAT, the change in NIM_RAT between t-1 and t, is close to zero for most bank groups,

although there are institutions experiencing a large change in net interest margins on a quarter-to-

quarter basis. The derivation of the change in NIM presented in equation (6) of section 3.1

30

shows

that

⎛ m EA f (y , t) + EA σ dz + y dEA − L f (r , t)− L σ dz − r dL ⎞⎜∑ k k k y k k k k k k r k k k ⎟ ⎝ k =1 k k ⎠ dEAtdNIM = − NIMt EAt

t EAt

This suggests that if the rate of change in EA is held constant, the change in NIM should be

inversely related to the level of prior-period NIM. The coefficient for the lagged value of

NIM_RAT is therefore expected to have a negative sign.

ROA is annualized after-tax net income for the quarter divided by average earning assets,

and DROA is the change in ROA from the previous quarter. Median ROA varies from 0.95 for

mortgage and consumer credit specialists to 2.33 for credit card specialists. Like DNIM_RAT,

the median DROA is close to zero; however, some large positive or negative numbers are

observed in the sample. DNONII_RAT is an annualized noninterest income for the quarter

divided by average earning assets, while DSECGL_RAT is annualized security gains and losses

for the quarter divided by average assets. Both variables proxy the effects of bank earnings

diversification on net interest margins. Signs of these variables could be positive or negative,

depending on whether these earnings are substituted for or complementary to NIM.

Finally, LOGAST is the log of total real assets derived as nominal assets deflated by the

urban consumer price index (CPI-U). Table 1 shows that there is a negative cross-section

relationship between the asset size of the bank within the group and the median NIM_RAT. This

relationship implies that, ceteris paribus, the asset size would be also negatively correlated to

DNIM_RAT, and therefore we expect the coefficient for LOGAST to have a negative sign.

However, as shown from the model development in section 3, a simple change in the scale of

operations for an individual bank should have no effect on changes in net interest margin.

31

4.2.5 Seasonality

As discussed in section 4.1, reported earnings of small banks tend to exhibit significant

seasonality. Reported ROA for these banks is consistently and significantly lower in the fourth

quarter of the year than in any other quarter. This pattern raises some questions about the

reliability of reported earnings for earlier quarters of the year. To control for these seasonal

patterns in reported earnings, we include three quarterly dummy variables. QTR2 takes a value

of one if the reported period is the second quarter, QTR3 if it is the third quarter, and QTR4 if it

is the fourth quarter.

4.3 Empirical specifications

Our empirical model of net interest margins is a one-way random-effects model and is

specified as follows:

yi,t = γ 1 yi,t−1 + β ′xi,t −2 +ϕ′zt−1 +τdquarter + vit

(8)

where i = 1, …, N, t = 1,…,T, vit = α i + uit . αi, is a random-disturbance term unique for the ith

observation, and both αi and uit are assumed to be normally distributed. yi,t is the dependent

variable, the change in NIM, xi,t−2 is a vector of bank-specific explanatory variables, zi ,t −1 is a

vector of financial market explanatory variables and dquarter are quarterly dummies. Finally, γ, β,

φ, and δ are a vector of coefficients. Section 4.2 has just discussed the expected signs of each of

these coefficients.

32

Following Brock and Franken (2002), bank-specific variables enter the model with two-

quarter lags; thus we avoid the potential endogeneity problems that may exist for these variables.

We estimate the model using the generalized-least-squares (GLS) technique, based on the

estimated disturbance variances. For dynamic random-effect models, the GLS estimator is

equivalent to the maximum likelihood estimator. The GLS estimator is consistent and

asymptotically normally distributed as the number of cross-sectional observations, N, approaches

infinity (Hsiao [2003]). N is very large for all the bank groups in our sample except international

banks, large noninternational banks, and credit card specialists. We address potential

heterogeneity and serial correlation problems in model specifications by controlling for the size

of the institution, applying cross-sectional random effects, and adding a lagged value of the

dependent variable. As an alternative to GLS estimation, we also tested the mixed-model

specification, which allows us to explicitly control for heteroscedasticity and serial correlation

problems in the unbalanced panel (Littell et al. [1996]). Within the mixed-model framework, we

tested for a potential bias arising from a number of institutions appearing only for a limited

number of quarters, a bias that was not controlled in the GLS specification, and we found the

effect to be insignificant. The results of the mixed-model specification were more or less similar

to those of the GLS estimation and are therefore not reported in this paper.

For each bank group, the empirical model for changes in net interest margins

(DNIM_RAT) to be tested is as follows:

DNIM _ RAT = c + β *VOL _1Y + β * ST _ Dummy + β * STGAP _ RAT + β * NM _ RATit 1 it −1 2 it −1 3 it − 2 4 it − 2 Interest Rate Risk + β * STGAP _ SD + β * NM _ SD5 it −1 6 t −1

Term Structure Risk + β * DS5Y _1Y + β * DS5Y _1Y + β * DS5Y _1Y + β * DS5Y _1Y7 t −1 8 t − 2 9 t −3 10 t −4

Credit Risk + β * DLN _ AST + β * DCI _ RAT + β * DCSPRD + β * DNPERF _ RAT11 t − 2 12 it − 2 13 t −1 14 it − 2

+ β * LOGAST + β * NIM _ RAT + β * DNIM _ RAT + β * DNONII _ RAT15 it −1 16 it − 2 17 it −1 18 it −2 19 t − 2 20 21 22+ β * DESCGL _ RAT + β * QTR2 + β * QTR3 + β * QTR4

(9)

33

The second empirical model we test measures the effect of interest-rate, term-structure,

and credit-risk shocks on overall profitability of the bank and has the same empirical

specification as the net interest margin model. We expect the ROA of banks with well-

diversified earning sources to be less sensitive to interest-rate and other shocks than net interest

margins. In other words, the better diversified a bank’s earnings are, the less significant are the

coefficients for most dependent variables; in other words again, bank earnings are expected to be

less sensitive to these shocks. The empirical model for changes in ROA (DROA) for each bank

group is specified as

DROAit = c + β1 *VOL _1Yit −1 + β2 * ST _ Dummyit −1 + β3 * STGAP _ RATit −2 + β4 * NM _ RATit −2 Interest Rate Risk + β * STGAP _ SD + β * NM _ SD5 it −1 6 t −1

Term Structure Risk + β * DS5Y _1Y + β * DS5Y _1Y + β * DS5Y _1Y + β * DS5Y _1Y7 t −1 8 t −2 9 t −3 10 t −4

+ β * DLN _ AST + β * DCI _ RAT + β * DCSPRD + β * DNPERF _ RAT Credit Risk 11 t −2 12 it − 2 13 t −1 14 it −2

+ β * LOGAST + β * NIM _ RAT + β * DNIM _ RAT + β *QTR215 it −1 16 it −2 17 it −1 18 (10)+ β * QTR3 + β *QTR4

We also test these models for stability over four separate subsample periods representing

changes in legislation that had effects on competition in the banking industry. These periods,

discussed more fully in the next section, are 1986–1988, 1989–1991, 1992 to the second quarter

of 1997, and the third quarter of 1997 to the second quarter of 2003.

19 20

5. The Results

Here we discuss the results first for the full sample period and then for the subsample

periods.

5.1 Full Sample Period results

34

Tables 2A and 2B summarize the results of cross-sectional time series regressions on

DNIM_RAT and DROA for each of the 12 bank groups. We applied the Hausman test for the

presence of one-way random effects for all bank groups. Except for international banks, we

cannot reject the presence of random effects for these groups of banks. The F-test shows that

one-way fixed effects exist for international banks. On the basis of these test results, we applied

one-way random-effects estimation to all bank groups other than international banks and applied

one-way fixed-effects estimation to international banks.

The statistical significance of explanatory variables and the size of coefficients for these

variables vary considerably across bank groups. The goodness of the fit for the DNIM_RAT

model measured by the modified R-square varies from 0.10 for consumer loan specialists to 0.37

for international banks, credit card specialists, and midtier nonspecialist banks. The goodness of

the fit for the DROA model varies from 0.32 for consumer loan specialists to 0.54 for small

nonspecialists with real assets greater than $300 million.

In general, the regression results presented in tables 2A and 2B imply that different types

of banks are sensitive to different types of shocks. Larger and more diversified institutions and

credit card specialists appear to be less vulnerable to interest-rate and term-structure shocks, but

still sensitive to credit shocks. Both of these relationships may reflect the greater use of off-

balance-sheet instruments that help these institutions hedge their interest-rate risk. In

comparison, agricultural banks, mortgage specialists, commercial loan specialists with real assets

less than $300 million, and small nonspecializing banks with real assets less than $300 million

are sensitive to all three types of shocks examined in this paper—credit, interest-rate, and term-

structure shocks.

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5.1.1 Sensitivity to Interest-Rate Shocks

The lagged ratio of net short-term assets (STGAP_RAT2) generally has a small negative

coefficient, when significant. The finding implies that, ceteris paribus, banks with longer-term

net assets experience greater variations in net interest margins. As found by Mays (1999), the

lagged ratio of nonmaturing deposits to earning assets (NM_RAT2) has a small positive

coefficient, when significant. These results suggest, as hypothesized, that the interest-rate

sensitivity associated with a bank’s funding has a significant, positive effect on the bank’s net

interest margins, regardless of the interest-rate environment. Two interaction terms included in

the model—STGAP_SD1 and NM_SD1—are designed to capture the marginal effect of an

increase in net short-term assets (STGAP_RAT2) and nonmaturing deposits (NM_RAT2) when

short-term interest rates rise (ST_DUMMY1 = 1). A negative coefficient for the short-term

interest-rate dummy variable (ST_DUMMY1), when considered together with interaction terms,

can be interpreted as showing that when short-term interest rates increase, there is an adverse

effect on the change in net interest margins for banks with no net short-term assets or

nonmaturing deposits. The two interaction terms, STGAP_SD1 and NM_SD1, have positive

signs for almost all bank groups and, when statistically significant, suggest that an increase in

short-term interest rates has an increasingly positive effect on the change in net interest margins

as the proportion of net short-term assets or nonmaturing deposits increases.

The economic significance of these coefficients also varies across the 12 bank groups.

For instance, in the case of C&I specialists, holding everything else constant, net interest margins

would be 6 basis points lower in the quarter following an increase in the interest rate. A 10

percent increase in STGAP_RAT2 or NM_RAT2 would offset that decline by 4 basis points.

For mortgage specialists, an increase in the short-term interest rate is followed by a 12-basis-

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point decline in NIM, with a 10 percent increase in STGAP_RAT2 or NM_RAT2 offsetting this

decline by less than 1 basis point and 3 basis points, respectively. Dissimilarities between C&I

specialists and mortgage specialists in the sensitivity of NIM to an increase in interest rates likely

reflect inherent differences in the maturity and interest-rate terms of the two groups’ loan

portfolios.

With a few exceptions, our two measures of interest-rate shocks—interest-rate volatility

(VOL_1Y1) and a short-term interest-rate dummy variable (ST_DUMMY)—have negative

coefficients, when significant. These results seem to contradict the findings of previous research

on determinants of net interest margins, which showed that interest-rate volatility positively

affects the level of net interest margins. However, the results are in line with our model that tests

for the effect of interest-rate volatility on the quarterly change in net interest margins. We find

that as we hypothesized in the equation (7), given the balance-sheet composition of banks in our

sample, higher interest-rate volatility lowers the change in net interest margins. The coefficients

are economically significant and vary widely across bank groups. A 1-percentage-point increase

in interest-rate volatility, measured by the standard deviation of one-year Treasury yields within

the quarter, is followed by about a 4- to 6-basis-point decline in NIM for most bank groups. The

coefficients are significantly larger for C&I specialists and credit card specialists, which tend to

have shorter-term and more default-risky assets. A 1-percentage-point increase in interest-rate

volatility leads to a 23-basis-point decline in NIM for C&I specialists and a 137-basis-point

decline in NIM for credit card specialists. These results also suggest that most banks are unable

to hedge against interest-rate risk effectively, at least in the short term. In comparison, mortgage

lenders that typically have assets with longer maturities appear to benefit from higher interest-

rate volatility. A 1 percent increase in interest-rate volatility leads to a 6-basis-point increase in

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NIM for mortgage specialists. In the next section, we show significant within-group variations

in banks’ sensitivity to interest-rate volatility across different regulatory and economic regimes.

5.1.2 Term-Structure-Shock Variables

Lagged changes in the Treasury yield spread (DS5Y_1Y1, DS5Y_1Y2, DS5Y_1Y3, and

DS5Y_1Y4) have positive and lingering effects on the change in net interest margins for

mortgage specialists and small nonspecialist banks with real assets greater than $50 million, up

to four quarters following the initial shock. On the other hand, none of the coefficients for the

four lagged values of the change in the Treasury yield spread is significant for credit card

specialists and midtier nonspecialist banks. For the remaining bank groups, the change in the

Treasury yield spread affects the variation in net interest margins only with a noticeable lag, and

one-quarter lagged change in the Treasury yield spread (DS5Y_1Y1) has a significantly negative

coefficient for some bank groups. For many bank groups, coefficients for two-quarter and three-

quarter lagged change in the Treasury yield spread (DS5Y_1Y2 and DS5Y_1Y3) are

significantly positive. For instance, ceteris paribus, a 100-basis-point increase in the yield spread

boosts NIM for mortgage specialists by 11 basis points two quarters after the initial shock, and 9

basis points three quarter after. In the case of small nonspecialists, the effects are similar but less

economically significant. A 100-basis-point increase in the yield spread leads to about a 6-basis-

point increase two quarters following the initial shock. These results suggest that banks that

have a large percentage of long-term fixed-rate assets, such as mortgages, are more vulnerable to

a flattening of the yield curve than other types of banks. These results also support our

hypothesis that portfolio composition, asset concentration, and business models, separately

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represented by bank groupings, are critical to an understanding of the effects of a term-structure

shock on bank net interest margins over time.

5.1.3 Credit-Shock Variables

The coefficient for the lagged value of the change in the ratio of loans to earning assets

(DLN_AST2) is positive and significant for most banks groups, as hypothesized. However, the

coefficient is significant but negative for agricultural banks, C&I specialists, commercial loan

specialists with real assets less than $50 million, and consumer loan specialists. On the basis of

the interpretation of this variable as a proxy for a size-preserving increase to higher earning

assets, a negative sign may imply either that these banks attract new loans by offering lower rates

or that they do not price the credit risk of new loans correctly or both. The results show that a

10-percentage-point increase in the loan-to-asset ratio typically accounts for a 2- to 4-basis-point

increase in NIM, although large noninternational banks benefit significantly more (8 basis

points) from the same increase.

The lagged value of the change in the C&I loan ratio (DCI_RAT2) has significantly

negative coefficients for commercial loan specialists with real assets over $300 million, other

small specialists, and small nonspecialist banks with real assets over $300 million. The negative

coefficient is contrary to prior expectations. It may reflect exogenous variables not specified in

the model, such as the competitive market landscape affecting loan pricing. Alternatively, for

this group of banks, a trade-off and diversification benefit may exist between an expansion to

higher-yielding assets and higher risk. Agricultural banks and mortgage specialists, however,

seem to benefit from expanding their C&I loan portfolios—a diversification effect for these

banks.

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The lagged value of a change in the credit spread (DCSPRD1) has a negative and

significant coefficient for most bank groups, a result suggesting that banks tighten underwriting

standards following credit market disturbances. In addition, despite the fact that banks do charge

a higher risk premium in response to higher credit risk, as shown in figure 5, banks are typically

unable to fully price credit risk and may instead rely on credit rationing. The effect of changes in

the credit spread appears to be economically significant for many bank groups, although there

are significant variations across groups. For instance, it is estimated that a 100-basis-point

increase in the credit spread subsequently reduces NIM by 5 basis points for CRE specialists, 16

basis points for C&I specialists, and 20 basis points for consumer specialists. As in the case of

interest-rate volatility, within-group results for the change in the credit spread vary significantly

across regulatory and economic regimes. These results are discussed in the next section.

With the exception of agricultural banks, the coefficient for the lagged value of the

change in the nonperforming asset ratio (DNPERF_RAT2) is negative, when significant. In

most cases, credit-quality deterioration, measured by DNPERF_RAT2, has considerably weaker

economic significance than the forward-looking loan-quality variable (DCSPRD1). However,

credit shocks appear to have particularly significant effects on credit card lenders, with a 1-

percentage-point increase in the nonperforming asset ratio leading to a 53-basis-point reduction

in NIM. This result may be primarily driven by subprime lenders that tend to be very credit

sensitive. Although several proxy measures for subprime lenders—such as a dummy variable to

indicate the top 5 percentile in terms of the loan yield—were considered, these variables were

ultimately dropped from the model because of data limitations. The results of credit-shock

variables suggest that, as we hypothesized in section 3, banks are unable to effectively price an

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unexpected increase in credit losses, and managers respond to this increase in the short term by

shifting funds to less default-risky and lower-yielding assets.

5.1.4 Other Institutional Variables

Other institutional variables have generally similar effects on the change in net interest

margins (DNIM_RAT) across bank groups, with some notable exceptions. The coefficient for

the lagged value of net interest margins (NIM_RAT2) is negative and significant at the 1 percent

level for all bank groups. This is in line with the expectation, as presented in equation (6), that

posits a negative correlation between the lagged level of net interest margins and the change in

net interest margins. The lagged change in net interest margins (DNIM_RAT1) has a significant

negative coefficient, implying error correction over time. Coefficients for DNIM_RAT1 and

NIM_RAT2 have the largest coefficients among all explanatory variables. Estimates show that

on average, a 100-basis-point increase in the lagged change in NIM leads to a 55-basis-point

increase in NIM in the subsequent quarter. On average, the 100-basis-point difference in two-

quarter lagged NIM translates to the 31-basis-point difference in the change in NIM on average.

The lagged value of the change in the noninterest income ratio (DNONII_RAT2) is

significant and positive for some groups, including large noninternational banks, agricultural

banks, CRE specialists, and commercial loan specialists with real assets less than $50 million;

however, it is significantly negative for the others, such as commercial loan specialists with real

assets over $300 million, other small specialists, small nonspecialist banks, and midtier

nonspecialist banks. This result shows that not all banks have reaped diversification benefits

from noninterest income.

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The coefficient for the lagged value of the change in security gains and losses

(DSECGL_RAT2) has a negative sign, where significant, except for mortgage specialists. This

implies that, except for mortgage specialists, security gains and losses are typically a

complementary source of earnings. However, for mortgage specialists, net interest margins and

security gains and losses seem to move together, perhaps because of a common response to

changes in short-term interest rates.

Finally, with the exception of midtier nonspecialist banks, the coefficient for the log of

total assets (LOGAST2) shows that the change in net interest margins is inversely related to asset

size, when significant. In other words, holding all else constant, the larger the bank in terms of

assets, the less sensitive the net interest margins will be with respect to a proportional change in